Extension of Khan’s homotopy transformation method via optimal parameter for differential difference equations. (English) Zbl 1442.65320

Summary: A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) [Y. Khan, “An algorithm for solving nonlinear differential-difference models”, Comput. Math. Model. 25, No. 1, 115–123 (2014; doi:10.1007/s10598-013-9212-z); Y. Khan and Q. Wu, Comput. Math. Appl. 61, No. 8, 1963–1967 (2011; Zbl 1219.65119)] via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems


Zbl 1219.65119
Full Text: DOI


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